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A STUDY ON MODELLING OF SLIDING FAILURE OF CONCRETE GRAVITY DAMS DUE TO EARTHQUAKE

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A STUDY ON MODELLING OF SLIDING FAILURE OF CONCRETE GRAVITY DAMS DUE TO

EARTHQUAKE

Susovan Sinha 1 , Dr. Aloke K. Datta 2 , Dr. Pijush Topdar 3

1Research Scholar, 2Associate Professor, 3Assistant Professor, Department of Civil Engineering, National Institute of Technology Durgapur, W.B (India)

ABSTRACT

Dams are probably the most important hydraulic structure generally constructed in the mountainous reach of river to generate hydropower. In this respect, a concrete gravity dam is designed to resist horizontal pressure of water held by it. Generally dams are constructed above a hard rock layer in hilly regions which are more susceptible zones of earthquake. So it is a great challenge to design a gravity dam against sliding failure due to earthquakes. Study of existing literature reveals that sliding displacement of a dam base depends on the friction coefficient at interface zone. Literature also suggests that even a small change in friction coefficient may lead to large differential displacement between the top of rock surface and bottom surface of the dam. Hence modelling of friction for sliding failure of dams, as above, is a critical area of research and further studies in this respect is important. In this paper, an effort is made to study on friction modelling at interface zone to set new guidelines for construction of gravity dams. In case of existing dams, there is a burning need for capacity enhancement through de-siltation. Therefore, existing dams may also be studied against sliding failure with such guidelines.

Keywords: Concrete Gravity Dam, Friction Modelling, Sliding Failure, Earthquake, De-Siltation.

I. INTRODUCTION

Generation of pollution free energy is one of the critical challenges face by technologists in the present scenario.

One of the possible source of pollution free energy can be hydro energy. Most developing nations like India has potential source of hydro-energy. This potential source of energy can easily be trapped by storing huge water in the hilly region. Storage of water can be done by constructing dams in those regions. Unfortunately these regions are vulnerable to high level of seismicity. Therefore construction of such type of heavy structure in these regions requires special attention as far as earthquake forces are concern. It is very much important that we have to design a dam which is strong enough in all respect of structural integrity. Foundation of concrete gravity dams is critical because it has to resist the high amount of stress generated at the junction of the base. Generally concrete gravity dams are constructed across a river and a layer of firm rock which is prepared by removing the looseriver deposits, is considered as the appropriate foundation of concrete gravity dam.So it is a great challenge to design a gravity dam against sliding failure due to earthquakes.

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This paper represents a critical review on the seismic effecton the stability of dam at interface zone between the dam base and the foundation rock and attempts to address the studies that have been conducted regarding the damage assessment and quantification, seismic vulnerability, risk analysis of dams and various possible measures adopted for minimizing the detrimental effects of earthquake. The paper reviews the latest technical information available on the earthquake effects on dam and the reviewis categorized under the following broad heads: (I) explanation about the adverse effects of earthquake on dams along with real life examples, (II) analysis of literature regarding state of the art studies on stabilityof dams against earthquakes, (III) study of the existing literature on the major factors contributing towards the sliding failure of dams, (IV) study of previous research on Friction modelling in the context of sliding failure and (V) existing literature on the effects of siltation on sliding due to earthquake for existing gravity dams.

Based on the above study in the context of sliding failure of concrete gravity dams due to earthquake, some important guidelines regarding proper modelling of such dams are suggested.

II. EXPLANATION ABOUT THE ADVERSE EFFECTS OF EARTHQUAKE ON DAM ALONG WITH REAL LIFE EXAMPLES

An earthquake (also known as a quake, tremor or temblor) is the unwanted shaking of the Earth's surface, which can be devastating enough to destroy major structures and kill thousands of life. The amount of the shaking of surface due to earthquake can range from barely felt to violent enough to toss people around. An earthquakes can destroy a whole city. Earthquakes are generated due to the sudden release of huge amount of energy in the Earth's crust which results in the generation of seismic waves.

The sliding displacement due to seismic force is a sensitive phenomenon to the value of the friction coefficient (µ) for the interface zone. Literature reveals that the base sliding displacement accumulates in the downstream direction when the shear strength of the interface zone is unable to resists the combination of hydrostatic forces and dynamic forces and the duration and characteristics of the free-field ground motion will govern the maximum sliding displacement. There is an inverse relationship between the maximum sliding displacement and coefficient of friction (µ). A dam on rigid foundation rock slides comparatively more than a dam on flexible foundation rock for a same value of ' µ ' [1]. Researchers also found that the ground motions with peak acceleration of 0.5 g may cause permanent sliding displacements of dams may range from a few inches to a couple of feet [2].

Hence it is a great challenge to enhance the stability of gravity dam against sliding failure due to the hydrostatic and dynamic forces, thereby maintaining the safety of the valuable hydraulic structure as well as the safety of neighbouring areas from the devastating effects of flood due to dam failure.

There are several real life examples of the devastating effects of earthquake on gravity dams and the same are discussed as follows;

2.1 The Hoover Dam

It is also known as the Boulder Dam has a height of 142 metre and having maximum reservoir impound capacity of 35Gm3 of water and this reservoir was first filled in the year 1935. In September 1936 the first seismic shocks were felt by this dam. Afterwards in few years other 100 shocks were felt when the height of the water within

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the reservoir reached a value of 120 metres. The reservoir height had been increased up to a height of 145 metres in the year 1938, and after 10 months on May 4th, 1939, a serious seismic shock of magnitude of 5 occurred when the volume of water within the reservoir reached reservoir normal capacity of 35 Gm3. In the following years seismic activity increased day by day.

Previously researchers had found that during a time period of 15 years before the first filling of the Lake, there was no reports of earthquake events in the area where the dam was constructed though said area had geological complexity[3].

2.2 The Kariba Dam

Its height is 125 metres, reservoir impounded capacity is 175 Gm3 of water and it covers an area of 6,649 square kilometres. The lake was formed over a geological formation made up of sediments and volcanic lava where several numbers of faults have been identified and mapped. In December during the year 1958 the first reservoir was started and was completed in August 1963. During the year 1959 and 1961 twenty-two and fifteen seismic shocks occurred, out of which one shock was there of magnitude 4 on the Richter scale. After that the recurrence of shocks has been increased and 63 shocks were encounteredup to March, 1962, and 61 shocks were felt during the first seven months of 1963. Researchers found that the magnitude of shocks increased day by day as the impounding volume of water within the reservoir increased [4].

In the year 1963 when the lake was filled stronger shocks having magnitude ranging within 6 to 6.1 were encountered having their epicentres located around the deepest part of the lake. Also after-shocks of magnitude 6 occurred due to previous seismic shock events. Afterwards 50 shocks were recorded in 1963 and 39 in the year 1968, and several shocks of different magnitude occurred during 1969 to 1970.

2.3 The Koyna Dam, India

The maximum reservoir capacity of the Koyna Dam is 2,780 million cubic metres (Mm3) and the height of the dam is 103 metres. In the year 1962 the first filling was done and ended in 1964, during that time the reservoir was half filled. The occurrence of seismic shocks increased during 1963, and for this dam also the location of epicentres was located under the reservoir or around the neighbouring area. During 1964 impounded volume of water in the reservoir was increased up to 2 Gm3. Afterwards in next few years the occurrence of seismic activities of low magnitude were recorded and after that it was predicted that no other devastating tremors will occur and everything had settled down.

During the Ninth Congress on Large Dams which was held in Istanbul, regarding the main cause of those seismic activities P.M. Mane, Chief Engineer at Koyna, stated that those tremors happened in the Koyna dam were probably due to “crustal adjustments” which occurred in and around the lake [5] and he also stated that the occurrence of seismic shocks decreases day by day and it is hoped that there will be no such tremors in future.

However, two major shocks were felt on 13th September, 1967, among those two the first caused huge damage to the Koynanagar village, killing 177 people and injuring 2,300 others. Large number of aftershocks were recorded, out of which one has a magnitude of 5.4 and its epicentre was located near the reservoir. Another shock of magnitude 6.4 occurred on 10th December, 1967.

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Regarding the geological formation researcher Rothe commented that the Koyna dam was built on the Deccan plateau with uniformly covered Basaltic rocks, and he termed that as the shield which is a least seismic zone of the world because there was no fault within the formation [6].

2.4 The Vaiont Dam, Italy

The features of Vaiont Dam is like that, height is 261metres and the volume of water retained by the reservoir is 150 Mm3. During the month of February, 1960 the filling was started and filling up to the maximum height was done in August, 1963. While the reservoir was partly emptied during 1961, there was no such seismic activities.

Afterwards in April, 1962 when water was filled up to the limit of 155 metres height, almost 15 shocks were recorded during April and May of that year.

Previous data revealed that there was 60 shocks within first 15 days ofSeptember 1963 when the water impounded height reached a value of 180 metres, during this specified time movement of earth started along the slope of Mont Toc above the lake. During October, 1963 the movement accelerated which results in a landslide causing generation of giant wave which flooded the lower valley portion, totally wiping out many villages and killing around 2,000 people.

2.5 Other examples

Other dams which are suspected of causing seismic shocks due to earthquakes include the Monteynard dam situated in the French and Alps and the Kremasta dam in Greece. For the former case, during April 1963an earthquake of magnitude 5 on the Richter was recorded when the reservoir was filled with water. In 1965 when the Kremasta reservoir was filled, a serious earthquake with a magnitude of 6.2 happened causing damage of around 500 residential buildings and killed one person and injured 60 other people.

In December 1976 the Teton, 95 metres high, collapsed caused the death of 14 people together with a damage of billion dollars, the failure of the 23 metres high Johnstown dam in Pennsylvania causing the death of over 2,000 people [7]. Malpasset dam near Frejus in Southern France failed on 2nd December 1959, led to the death of 421 people[8]. The failure of St. Francis dam in California, which causing the death of 300 people, has been attributed to faulty foundations with the combination of seismic force[9].

III. ANALYSIS OF LITERATURE REGARDING STATE OF ART STUDIES ON STABILITY OF DAMS AGAINST EARTHQUAKES

Up to the present time, a small number of seismic events, some of them with magnitudes close to 6 (Richter), have been strong enough, to cause not only widespread concern but also damage to structures, including in at least one case damage to the dam itself. Nevertheless, in most cases the filling of reservoirs has not been accompanied by any significant increase in any type of seismicity. Therefore, it is believed that special geotechnical and/or hydro-geological conditions are required for the triggering of earthquakes of engineering importance” [10].

“In the present state of knowledge regarding the seismic effects associated with reservoir loading, it is impossible to predict with certainty whether hazardous earthquakes are likely to be triggered by the filling of a large reservoir” [11].

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France’s 110metres high Vouglans dam whose reservoir has a maximum volume of 605 Mm3 of water, filling began in April 1968, and was completed by November 1969. The reservoir was partially emptied from December, 1970 to March, 1971, and was refilled very rapidly, reaching maximum capacity in June, 1971.

Almost immediately on 21st Junean earthquake occurred with a magnitude of 4.5. It was followed by 20 or so tremors between 21stJune and 2ndJuly. Significantly, the epicentre was situated 5 km to the south east of the reservoir. Previously, no seismic activity has been known in the region [12].

A case is point in California’s Oroville dam. Since the occurrence of an earthquake in 1975, there has been regular seismic activity within a 20 km radius of the dam. That activity as P. W. Morrison of the California Department of Water Resources, observes in a paper written jointly with T.R. Toppozada of the California Division of Mines and Geology, “decreased markedly during winter and spring filling of the lake and increased during summer and fall drawdown” [13].Interestingly enough, during the 1975 earthquake also occurred during the summer drawdown which followed the refilling of the reservoir. Commenting on that association, Morrison and Toppozada argue: “These observations suggest that filling Lake Oroville results in fault stability, but that during drawdown, instability occurs when the decrease in load stress significantly exceeds the slower decrease in subsurface pore pressure. Seismicity accompanying the summer drawdown has decreased steadily since the August 1975 earthquake, suggesting that the rupture zone of this earthquake has been largely relieved of stress”

[14].

There also appears to be heavy cracking in the rocks of the river gorge where the Tehri dam is to be built. Those rocks, according to V. D. Saklani, President of the Tehri Bandh Virodhi Sangharsh Samati, are “most unlikely to be able to bear the weight of (the) 2.62 million acre feet of water to be impounded in the lake” [15].

Therefore it is clear enough that from the past to the recent time, the dam stability became questionable due to various earthquake events. Literature suggested that the stability of the dam hampers due to the inferior geological conditions of the dam foundation and interestingly thing was that, there was a relation between the occurrence of earthquake and the cyclic filling and empting of the reservoir.

IV. STUDY OF THE EXISTING LITERATURE ON THE MAJOR FACTORS CONTRIBUTING TOWARDS THE SLIDING FAILURE OF DAM

Any concrete gravity dam would be stable against hydrostatic forces and dynamic forces if the value of the coefficient of friction for the interface zone between the dam base and the foundation rock is considerably high especially for moderate to tall dams, because the interlocking between dam-foundation rocks generally reduces the response of the earthquake. There is an inverse relationship between the maximum sliding displacement and coefficient of friction (µ). A dam on rigid foundation rock slides comparatively more than a dam on flexible foundation rock for a same value of ' µ '[1].

Researchers investigated that the permanent sliding displacements of dams induced by ground motions with peak acceleration of 0.5 g may range from a few inches to a couple of feet[2]. The seismic performance of concrete gravity dams regarding base sliding affected by the effects of dam– foundation contact conditions.

Thus, it is very important that analytical models used in seismic evaluation of concrete gravity dams explicitly consider the effects of dam–foundation contact conditions during seismic excitations [16].

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The study of Seismic induced slip of concrete gravity dams at the rock interface is often required if there is a presence of weak rock joints immediately underneath the surface which can be predicted by developing an empirical formula. With the help of detailed finite element runs the proposed formula was validated for fair prediction of the seismic-induced slip for all typical sections of concrete gravity dams, such as bulkheads, sluiceways, log-chutes, and headworks/ powerhouses[17].

There are various methods by which the tendency of sliding failure due to seismic force can be analysed. But to reduce the said tendency or to enhance the anti-sliding stability of gravity dam, the role of frictional force is very much important and hence there is a broad area of future research work on modelling the friction parameter in the interface zone between dam foundation and rock layer below the foundation.

V. STUDY OF PREVIOUS RESEARCH ON FRICTION MODELLING IN THE CONTEXT OF SLIDING FAILURE

Previously various researchers made their effort to model the Friction parameter between the dam foundation and underneath rock layer and their findings are discussed below:

Block model representations is the unique way to analyse the rock mass behaviour by discrete element models.

But the selection of joints within the rock mass and model the same is a complex thing and need simplification while considering non-planar or non-persistent joints[18].

The frictional behaviour of rocks is analysed and simulated previously by the finite element code using the node-to-point contact element concept to analyse the frictional contact between multiple finite deformation rock mass with stick and finite frictional slip and by performing practical experiments with rock the frictional instability phenomena, geometrical effects on frictional behaviour were established[19].

Previously researchers pointed out that though the determination of both static and kinetic friction coefficients in laboratory condition can be done with little difficulties, it is difficult enough to determine the time and condition dependent features of coefficient of friction for both clean and lubricated surface. Hence the friction have to be modelled very carefully because the stability of friction force depends on the type of contact conditions [20]. Researchers made effort to evaluating the hydro-mechanical behaviour of a gravity dam against the typical cycle of reservoir filling and emptying by a distinct element method (DEM) numerical model. As various rock wedges with different geological characteristics present in the foundation, hence the factor of safety against sliding of the gravity dam was also evaluated using the DEM model. They concluded that due to the presence of jointed rock and cracks within the rock layers, the factor of safety of dam get reduced [21].

The deformation properties of weak foundation bed below the dam was simulated previously considering an anisotropic laminar elemental layer with specified thickness and another simulation was also done to pointed out position of joints and fissures present in the rock mass considering the contact friction interface element without any thickness at the interface zone between dam foundation and rock layer. For highconcretegravity dam the resistance against sliding at the foundation interface zone was analysed by nonlinear finite element method (FEM). To evaluate the instability of dam’s foundation system the strength reserve factor (SRF) method was adopted and ultimate conclusion was like that, dam failure was related to the weakness of the supporting layer present below the dam foundation [22].

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Researchers also found that the cyclic loading is an important factor for determining the characteristics of the interfaces zone between structural and geological materials and also the joints, faults present in the rock mass and thus cyclic loading also governs the analysis of engineering structures. They also commented that, appropriate laboratory tests has to be performed to recognise the influenceof relative motions at interfaces.

Finally concluded from the calculation coming out from the tests that, various factors such as number of loading cycles, relative density of sand, normal stress etc. influenced the cyclic interface behaviour at the interface zone

[23].

Regarding the limiting contact friction between various constructional materials and supporting foundation layer, previously researchers stated that, with the increase in surface roughness and the angularity of the grains of geological formations, the coefficient of friction also increased, and also with the increase of particle size the roughness of the contact surface increases[24].

VI. EXISTING LITERATURE ON THE EFFECTS OF SILTATION ON SLIDING DUE TO EARTHQUAKE FOR EXISTING GRAVITY DAMS

Siltation is defined as the pollution of water by fine particulate terrestrial elastic material, with a less particle size grains, generally dominated by silt or clay. It refers both to the increased concentration of suspended sediments, and to the increased temporary or permanent accumulation of fine sediments on bottoms where they are undesirable.

Previously researchers analysed that for small to medium sizereservoirs of Australian continent (having catchment area less than 100 km2) a load with very high magnitude was created by the combined effects of the sediment load and the major flood events, especially for thin concrete structures and for that reason the dam safety becomes questionable [25]. Reservoir siltation affects the safety of old reservoirs and also reduces the storage capacity resulting increased outflow and increased head above crest for a given reservoir inflow. Figure 1 shows how the sediment weight and larger head above crest creates higher pressure on dam wall.

Figure 1:- Effects of reservoir siltation on dam wall pressure.

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Farzad Bandei et.al realised the complexity of considering the sediment load in their model and to analyse the Dynamic Interaction of Dam-Sediment the Substructure method was used. A series of simple sub interaction was used here to analyse the interaction of dam-sediment. Then using the superposition principle of force the results are combined to each other [26] and an assumption was made as the interaction was happened just at the boundary of the substructures [27].

However it will be very much difficult topoint out the adverse effect due to seismicity on gravity dam wall by partially and fully loose sediment layers within the reservoir because those sediment layers will acts as a material between liquid and solid state, hence this will be an important area of research regarding the dam stability against seismic force.

VII. CONCLUSION

The brief description of the conclusions coming out from the previous sections is like that, the main key parameter regarding the stability of concrete gravity Dam against sliding failure due to the hydrostatic forces and dynamic forces is the coefficient of friction or the friction of the interface zone between the dam base and the foundation rock. While being a very sensitive parameter, the modelling of friction is a critical area of research for the seismic stability analysis of existing gravity dams as well as dams to be constructed in future.

However this friction modelling done previously by various techniques such as Mohr-Coulomb criterion, Coulomb’s friction law, Newmark’s sliding block analysis, Fluid-Foundation-Structure Interaction simulation with the finite elements method, Richards-Elms and Wong empirical formula etc., future scope of study will be there to find out the best method for dam stability analysis against seismic force and model the friction parameter in this regard.

Based on critical review of existing literature it appears that failure of dams due to sliding is still a grey area of research. To establish a realistic concept on sliding failure and friction modelling the following guidelines are required to be incorporated through farther studies;

(i) Friction like phenomenon at the interface zone particularly in gravity dam attracts some critical issues viz.

wet friction with flow of waters with high speed in the interface zone. Proper modelling should be developed in this respect.

(ii) In case of existing dams siltation is a matter of prime concern. In studding sliding like phenomenon due to earthquake forces effect of loose mass(between liquid and solid) can be an adverse condition. Proper modelling with the incorporation of effect of additional loose mass will enhance the existing methodology.

(iii) Generalised and simple procedures are required for easy implementation in design of gravity dam against sliding like fail.

VIII. ACKNOWLEDGMENTS

The writers gratefully acknowledge the facilities provided by the National Institute of Technology Library e- resources for gathering the study materials.

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IX. NOTATION

The following symbols are used in this paper:

E = Energy generated due to Earthquake disturbance, in ergs or in 10-7 Joules in S.I unit FEM = Finite element method

g = Acceleration due to gravity, in metre/sec2 Gm3 = Billion cubic metres

M = Earthquake magnitude Mm3 = Million cubic metres µ = Co-efficient of friction

REFERENCES

[1]. Chávez, J. W., & Fenves, G. L.,“Earthquake response of concrete gravity dams including base sliding”, Journal of Structural Engineering, 121(5), 1995, pp. 865-875.

[2]. Chopra, A. K., & Zhang, L.,“Earthquake-induced base sliding of concrete gravity dams”, Journal of structural Engineering, 117(12),1991,pp. 3698-3719.

[3]. Rothe. J. P., “Fill a Lake, start an Earthquake”, New Scientist, Vol. 39 No. 605, 1978, pp.78.

[4]. Rothe. J. P., “Summary: Geophysics Report’ in William C. Ackermann et. al. (Eds),Man-Made Lakes, Their Problems and Environmental Effects”, American Geophysical Union, Washington DC, 1973, pp.441-442.

[5]. Mane, P. M.,“Earth tremors in Koyna Project area”. In Cong. on Large Dams, 9th, Proc. C, Vol. 13, 1967, pp. 509-517.

[6]. Rothe, J. P.,op.cit., 1973, pp.446.

[7]. Philip Williams, “Dam Design; is the technology faulty?” New Scientist, 2 February 1978.

[8]. Rothe. J. P., personal communication to Edward Goldsmith, 1983.

[9]. Widstrand. C, “Conflicts over Water”, in Carl Widstrand (Ed), Water Conflicts and Research Priorities, Pergamon, Oxford, 1980, pp.147.

[10]. UNESCO Working Group on “Seismic Phenomena associated with Large Reservoirs”, Report of First Meeting, UNESCO, 14-16 December 1970, SC/CONF. 200 4, Paris, 6 March 1971, pp.3.

[11]. UNESCO Working group on “Seismic Phenomena associated with Large Reservoirs”,Report of Second Meeting, UNESCO, SC-71/CONF. 42/3, 14-17 December 1971, pp.4.

[12]. Rothe, J. P., “Note sur les seismes de Vouglons”, unpublished paper, June-July 1971.

[13]. Toppozada, T. R., &Morrison Jr, P. W.,“Earthquakes and Lake Levels at Oroville Butte Cao.

California”, Earthquake Notes Vol. 52 No. 1, 1981, pp. 27.

[14]. Ibid, pp.28.

[15]. Saklani,.V. D. “Tehri Dam Project that spells disaster”, Tehri Bandh Virodhi Sangharsh Samiti, Tehri Garhwal,1989, pp.viii.

[16]. Ouzandja, D., & Tiliouine, B.,“Effects of Dam–Foundation Contact Conditions on Seismic Performance of Concrete Gravity Dams”, Arabian Journal for Science and Engineering, 2015, pp. 1-10.

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[17]. Danay, A., & Adeghe, L. N.,“Seismic-induced slip of concrete gravity dams”, Journal of Structural Engineering, 119(1), 1993, pp. 108-129.

[18]. Lemos, J. V.,“Block modelling of rock masses: Concepts and application to dam foundations”, European Journal of Environmental and Civil Engineering,12(7-8), 2008, pp. 915-949.

[19]. Xing, H. L., Mora, P., & Makinouchi, A.,“A unified friction description and its application to the simulation of frictional instability using the finite element method”, Philosophical Magazine, 86(21-22), 2006, pp. 3453-3475.

[20]. Blau, P. J.,“The significance and use of the friction coefficient”, Tribology International, 34(9), 2001, pp.

585-591.

[21]. Gimenes, E., & Fernández, G.,“Hydromechanical analysis of flow behaviour in concrete gravity dam foundations”, Canadian geotechnical journal,43(3), 2006, pp. 244-259.

[22]. Wei, Z., Xiaolin, C., Chuangbing, Z., & Xinghong, L.,“Failure analysis of high-concrete gravity dam based on strength reserve factor method”, Computers and Geotechnics, 35(4), 2008, pp. 627-636.

[23]. Desai, C. S., Drumm, E. C., & Zaman, M. M.,“Cyclic testing and modelling of interfaces”, Journal of Geotechnical Engineering, 111(6), 1985, pp.793-815.

[24]. Leonards, G. A., & Brumund, W. F.,“Experimental study of static and dynamic friction between sand and typical constuction materials”, Journal of Testing and Evaluation, 1(2), 1973, pp. 162-165.

[25]. Chanson, H., & James, D. P.,“Siltation of Australian reservoirs: some observations and dam safety implications”,In 28th IAHR Congress, January, 1999.

[26]. Hariri, M., Mirzabozorg, H.,, "Effects of near fault ground motions in seismic performance evaluation of a symmetric arch dam", soil mechanics and foundation engineering, Vol. 49, No. 5, Russian, 2012.

[27]. Bandei, F., Azizian, G., & Golbarari, M. H., "Displacement of Gravity Dam in Far and Near Fault Earthquake Including Dam-Water-Sediment-Foundation Interaction", Current World Environment, 10(Special Issue 1 (2015), pp. 955-966.

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